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C₂×#37132 #7634489

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

8810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

(1,2);(4,6)(7,8,10,11)(9,13,14,12)(16,20)(18,22);(8,11)(12,13)(16,20)(17,21);(3,4,5,6)(15,16,19,20)(17,18,21,22);(7,8)(9,12)(10,11)(13,14)(15,17,19,21)(16,18,20,22);(7,9,10,14)(8,12,11,13)(15,18)(16,21)(17,20)(19,22)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541685);